Measurement & Scaling Techniques

Measurement

• Measurement is a process of mapping aspects of a domain onto other aspects of a range according to some rule of correspondence.

• In measuring, we device some form of scale in the range and then transform or map the properties of objects from the domain onto this scale.

• Nature of data1. Nominal data2. Ordinal data3. Interval data4. Ratio data

Measurement Scales Scale Number System Marketing

PhenomenaPermissible

Statistics

Nominal Scale Unique definition of numerals(0,1,2,…,9)

Brands,Male – Female,Store type,Sales territories.

Percentages,Mode, Binomial test,Chi-square test.

Ordinal Scale Order of numerals(0<1<2< … <9)

Attitudes,Preferences,Occupation,Social class.

Percentile, Median, Rank-order-correlation.

Interval Scale Equality of difference( 2 – 1 = 7 – 6)

Attitudes, Opinions,Index numbers.

Range, Mean, Standard deviation,Product-moment correlation.

Ratio Scale Equality of ratios ( 2/4 = 4/8)

Age, Costs, No of customers,Sales (units/Rs).

Geometric mean,Harmonic mean,Coefficient of variation.

Sources of Error in Measurement

a) Respondentb) Situationc) Measurerd) Instrument

Tests of Sound Measurement

1. Test of Validityi) Content validityii) Criterion-related validitya) Predictive validityb) Concurrent validityiii) Construct validity2. Test of Reliability3. Test of Practicality

Scaling

Meaning of Scaling• Scaling describes the procedures of assigning numbers to

various degrees of opinion, attitude and other concepts. • This can be done is two ways, viz.,i. Making a judgement about some characteristic of an

individual and then placing him directly on a scale that has been defined in terms of that characteristic, and

ii. Constructing questionnaires in such a way that the score of individual’s responses assigns him a place on a scale.

Scale Classification Bases a) Subject Orientation - Under it a scale may be designed to measure characteristics

of the respondent who completes it or to judge the stimulus object which is presented to the respondent.

b) Response Form - Under this we may classify the scales as categorical and

comparative. Categorical scales are also known as rating scales, & comparative scales are also known as ranking scales.

c) Degree of subjectivity - With this basis the scale data may be based on whether we

measure subjective personal preferences or simply make non-preference judgement.

Scale Classification Bases d) Scale properties - Based on this, one may classify the scales as nominal,

ordinal, interval or/& ratio scales. e) Number of dimensions - On this basis, scales can be classified as ‘unidimensional’ and

‘multidimensional’ scales. f) Scale construction techniques Arbitrary approach Consensus approach Item Analysis approach Cumulative scales Factor scales

Important Scaling Techniques1) Rating Scales• The rating scale involves qualitative description of a limited

number of aspects of a thing or of traits of a person.• When we use rating scales, we judge an object in absolute

terms against some specified criteria. • These ratings may be in following such forms: “like – dislike”; “above average – average – below average”; “like very much – like somewhat – neutral – dislike

somewhat – dislike very much”; “ excellent – good – average – below average – poor”; “ always – often – occasionally – rarely – never”; etc.

Rating Scales• Rating scale may be either a graphic rating scale or an

itemized rating scale. i) Graphic Rating Scale Example: How do you like the product? (Please check)

Like very much

Dislike some what

Like some what

Neutral Dislike some what

Rating Scales

ii) Itemized Rating ScaleExample: Suppose we wish to inquire as to how well does a

worker get along with his fellow workers? Alternatives: • He is almost always involved in some friction with a fellow

worker• He is often at odds with one or more of his fellow workers• He is sometimes gets involved in friction• He infrequently becomes involved in friction with others• He almost never gets involved in friction with fellow workers

Important Scaling Techniques2) Ranking Scales • Under ranking scales, we make relative judgement against

other similar objects. • The respondents under this method directly compare two or

more objects and make choices among them.• There are two generally used approaches of ranking scales,

viz., a) Method of paired comparisons b) Method of rank order

Ranking Scalesa) Method of paired comparisons• Under it the respondent can express his attitude by making a

choice between two objects, say, between a new flavour of soft drink & an established brand of drink.

• But, when there are more than two stimuli to judge, the number of judgement required in a paired comparison is given by:

N = n(n – 1)/2 where N = number of judgement n = number of stimuli or objects to be judged.

Ranking Scales

a) Method of paired comparisons• Composite Standard MethodExample: Suppose there are four proposals which some union

bargaining committee is considering. The committee wants to know how the union membership ranks these proposals. For this purpose a sample of 100 members might express the views as shown in the following table:

Composite Standard Method

Suggestion

A B C D

ABCD

--404580

65--5020

3238--98

204270--

Total 165 135 168 132

Rank Order 2 3 1 4

Mp 0.5375 0.4625 0.5450 0.4550

Zj 0.09 (-)0.09 0.11 (-)0.11

Rj 0.20 0.02 0.22 0.00

Comparing the total number of preferences for each of the four proposals, we find that C is the most popular.

Composite Standard Method Steps:(i) Using the above data, we work out the column mean with the

help of the following formula: Mp = [C + 0.5(N)]/nN = [165 + (0.5)(100)]/4(100) = 0.5375where, Mp = the mean proportion of the columns, C = the total number of choices for a given suggestion, n = number of stimuli (proposals in the given problem), N = number of items in the sample.

(ii) Find Zj values for Mp from the table giving area under the normal curve.

Composite Standard Method Steps:(iii) Assign zero to lowest value and find out Rj (ranks).This can be shown in scale as below:

D

0.30.20.10.0 0.4

B A C

Ranking Scalesb) Method of Rank order• This method is easier and faster than the method of paired

comparisons stated above.• For example, with 10 items it takes 45 pair comparisons to

complete the task, whereas the method of rank order simply requires ranking of 10 items only.

• The problems of transitivity (such as A prefers to B, B to C, but C prefers to A) is also not there in case of rank order.

Different Scales for Measuring Attitudes of People

S.N. Name of the Scale construction approach

Name of the scales developed

1 Arbitrary approach • Arbitrary scales

2 Consensus scale approach • Differential scales (such as Thurstone Differential scale)

3 Item analysis approach • Summated scales (such as Likert scale)

4 Cumulative scale approach • Cumulative scales (such as Guttman’s scalogram)

5 Factor analysis approach • Factor scales (such as Osgood’s Semantic Differential, multi-dimensional scaling, etc.

1. Arbitrary Scales:

• Arbitrary scales are developed on ad hoc basis and are designed largely through the researcher’s own subjective selection of items.

• The researcher first collects few statements or items which he believes are unambiguous and appropriate to a given topic and then people are asked to check in a list the statements with which they agree.

Merits:1. They can be developed very easily, quickly and with relatively less

expense.2. They can also be developed to be highly specific and adequate. Limitation: We do not have objective evidence that such scales measure

the concepts for which they have been developed. We have simply to rely on researcher’s insight and competence.

2. Differential Scales (or Thurstone-type Scales):

• The name of L. L. Thurstone is associated with differential scales which have been developed using consensus scale approach.

• Under such an approach the selection of items is made by a panel of judges who evaluate the items in terms of whether they are relevant to the topic area and unambiguous in implication.

Merits: 1. To measure attitudes towards varied issues like war, religion, etc.2. Considered most appropriate and reliable when used for measuring a

single attitude. Limitations:1. Very high cost and effort required to develop them.2. The values assigned to various statements by the judges may reflect their

own attitude.

3. Summated Scales (or Likert Scale):

• These are developed by utilizing the item analysis approach whrein a particular item is evaluated on the basis of how well it discriminates between those persons whose total score is high and those whose score is low.

• Thus, summated scales consist of a number of statements which express either a favourable or unfavourable attitude towards the given object to which the respondent is asked to react.

• In this method response category often consists of numerical values 1,2,3,4,5. These five points constitutes a scale.

3. Summated Scales (or Likert Scale):

• At one extreme of the scale there is strong agreement with the given statement and at the other, strong disagreement, and between them lie intermediate points. We may illustrate this as under:

Advantages: 1. Relatively easy to construct than Thurstone-type scale since it can be

performed without a panel of judges.2. Considered more reliable & also provides more information & data.3. Easily used respondent-centred and stimulus-centred studies.

DisagreeUndecidedAgreeStrongly agree

Strongly disagree

1 2 543

3. Summated Scales (or Likert Scale):Limitations: 1. With this scale, we can simply examine whether respondents are more or

less favourable to a topic, but we cannot tell how much more or less they are.

2. There is no basis for belief that the five positions indicated on the scale are equally spaced.

Example: In making a choice of toilet soap the following factors are found to be very important. Please indicate your opinion that describes your feeling:

Factor Strongly agree

Agree Neutral Disagree Strongly disagree

1. Fragrance

2. Price

3. Leather

4. Effect on skin

5. Lasting

4. Cumulative Scales (Louis Guttman’s Scalogram Analysis)

• Consists of series of statements to which a respondent expresses his agreement or disagreement.

• The special feature of this type of scale is that statements in it form a cumulative series.

• Scalogram analysis refers to the procedure for determining whether a set of items forms a unidimensional scale.

5. Factor Scales

• An important factor scale based on factor analysis is; i) Semantic Differential Scale, and ii) Multidimensional scaling.

i) Semantic Differential Scale:

• Developed by Charles E. Osgood, G. J. Suci and P. H. Tannenbaum in 1957.

• Here the subjects are asked to indicate their choice among a set of bi-polar phrases for adjectives that best describes their feelings towards an issue/object.

• Like in Likert scale, a set of statements are constructed, but the responses consist of a set of opposite meaning phrases at the two extreme ends of the scale.

• This scaling consists of a set of bi-polar rating scales, usually of 7 points, as shown under:

i) Semantic Differential Scale:

Heavy

LenientSevere

UnsuccessfulSuccessful

Unsocial

ColdHot

Light

Passive

Social

Active

Strong

Progressive

Weak

Regressive

Slightly

0123

Quite ExtremelyQuiteExtremely

-3-2-1Neither

NorSlightly